Part 1: Passé composé with the auxiliary verb avoir

J’ai mangé I ate I have eaten

Hier, j’ai mangé des pâtes: Yesterday, I ate pasta. J’ai mangé des pâtes trois fois dans la semaine: I have eaten pasta three times in the week.In both examples, it is a past event not related to a duration or repetition.

Place of the adverb: I have eaten well: J’ai bien mangé Place of the pronoun: You ate it: tu l’as mangé

A. Invariable

Elle a joué Nous avons chanté Vous avez parlé

The past participle is invariable as there is no agreement between it and the subject of the sentence

B. Agreement

Important: There is an agreement but with the direct object when there is one and it is placed before the verbs.

Direct Object: I ate apples Apples is the direct object (direct because there is no preposition before)

J’ai mangé des pommes (here des is the plural of the indefinite article une) The pronoun used to replace Pommes is les Je les ai mangées ( I ate them)Les is feminine plural and placed before the verbs so there is an agreement with the past participle: mangées

Les pommes que j’ai mangées (again Pommes is before)

To go further:

J’ai écrit à mes enfants: I wrote to my children Écrire is a prepositional verb, so no agreement, even if the pronoun is before: Je leur ai écrit But J’ai écrit une lettre à mes enfants, in this sentence there are a direct (lettre) and an indirect object (enfants) Je la leur ai écrite: the agreement is between la placed before the verbs abs the past participle.